Turing's celebrated 1950 paper proposes a very general methodological criterion for modelling mental function: total functional equivalence and indistinguishability. His criterion gives rise to a hierarchy of Turing Tests, from subtotal ("toy") fragments of our functions (t1), to total symbolic (pen-pal) function (T2 -- the standard Turing Test), to total external sensorimotor (robotic) function (T3), to total internal microfunction (T4), to total indistinguishability in every empirically discernible respect (T5). This is a "reverse-engineering" hierarchy of (decreasing) empirical underdetermination of the theory by the data. Level t1 is clearly too underdetermined, T2 is vulnerable to a counterexample (Searle's Chinese Room Argument), and T4 and T5 are arbitrarily overdetermined. Hence T3 is the appropriate target level for cognitive science. When it is reached, however, there will still remain more unanswerable questions than when Physics reaches its Grand Unified Theory of Everything (GUTE), because of the mind/body problem and the other-minds problem, both of which are inherent in this empirical domain, even though Turing hardly mentions them.